Civil Engineering May 2019 [~]tmlW IINYATIONt Algebra 1

..
be 28 years more than A's age by then. How old reached B 4 hours after they passed each other, 24. A train, an hour after starting, had an accident
is A now? Answer: 28 yrs old the second reached A 2 houts and 15 minutes and was detained for an hour, after which it
/ 10. At present, the sum of the parents' ages is twice after they passed. Find the time that each train proceeded at 3/5 oftts former rate and arrived
the' sum of the children's ages. Five years ago, required to make the trip. 7 hrs and 5.25 hrs at the destination three hours after the time.
the sum of the parents' ages was 4 til;nes the Had the accident happened 50km farther on the
16. Simplify: 7(2x)-B( 2x-l) Ans: 10/3 Jine, it would have arrived one and one-half
sum of the children's ages. Fifteen years from 2x+J -2x-l
now, the sum of the parents' ages will be equal . hours sooner. Find the length of the journey.
17. Two students attempted ·to solv.e a problem . Ans: 88.89 km
to the sum of the children's ages. How many
which reduces into a quadratic equation. One,
children are there? Answer: s 25. In the expansion of (x 1l 2 - 3r3/ 2) 12, find the term
in simplifying, made a mistake in the constant
~ / 11. In 1930, the following question was proposed: free of x. Ans: --5940
term and had -2 & 6 for his roots. The other
A man's age at death was one twenty-ninth of made a mistake in the coefficient of the first- 26. If the middle term of the expansion of (x 3 + 2y2)n
the year of his birth. How old was he in the year degree term and had -3 & 5 for his roots. What is Cx18y12, find C. Ans: 59,136
1900? Answer: 44 yrs old is the correct quadratic equation? 27. Two £rains, one 350 ft long, the other 450 ft long,
/ 12. A certain physicist, who is always in a hurry, Answer: x2 - 4x - 15 = 0 on parallel tracks, can pass each other
walks up an ongoing escalator at the rate of one 18. Find the sum of the coefficients of the terms in completely -in 8 seconds when -moving in
step per second. Twenty steps bring him to the the expansion of (4x - 3) 8. Ans: -6560 opposite directions. When moving in the same
top. Next day he goes up at two steps per 19 .. Mang Andoy has lived one-fourth of his life as direction, the faster train completely passes the
second, reaching the top in 32 steps. How a boy, one-fifth as a youth, one-third as a man, slower one in 16 seconds. Find the speed of the
many steps are there in the escalator? Ans: 80 and has spent 13 years in his dotage. How old faster train. Ans: 75 fps

/ 13. A man was enjoying the afternoon rowing is he?" Ans: 60 28. ' A battleship started on a 500-miie voyage but
leisurely upstream when his baseball cap fell in 20. A and B run around a circular track whose was brought to full stop an hour after starting
. the water. So absorbed was ·he in listening to circumference is 150m. \.\Then they run in for military reasons, delaying it for full hour,
the music frol}l his earphones that it was 12 opposite directions they meet every 5 seconds, after which it was ordered to proceed at a
mint,1tes before he discovered his cap missing. but when they run in the, same direction from reduced velocity equivalent to 75% of its
He turned around and recovered the cap 1 km the same point they are together every 25 former rate. The ship arrived at its destination
downstream from where it fell. Assuming seconds. What are their rates? 3 hours and 3 quarters after scheduled time. If
constant speed and neglecting the time for Ans: 18m/ s and 12m/ s it was desired for the ship to arrive ·one hoq..r
turnaround, what was the speed of the_water 21. An airplane takes 1.5 hours to travel 600 mi, and a quarter sooner, how far from the
current? Answer: 2.5 kph with the wind and 1.6 hours to fly back. Find destination should the ship have ·been ordered
the speed· of the plane. stopped? Ans: ·243.24mi.
/ 14. A train, an hour after star.ting, had to stop due Ans: 387.5mph
to some engine trouble. After one hour, H Situation 1. Allan can cover a circular track in 50
22. A boatman rows to a place 48 km distant and
proceeded at 60% of its former rate and arrived seconds while Brando can cover the same track
back in 14 hours; he finds he can row 4km with in 40 seconds. Going in the same direction, find
3 hours after the time. Had the incident the stream in the same time as 3 km against the the time they· wql be together if:
happened 50km farther on the line, it would stream. Find the rate of the stream. Ans: I kph 29. Brando gives Allan a head start of 5 seconds.
have arrived 1.5 hours sooner. Find the length · Ans: 20 sec of Brando
23. A policeman is pursuing a snatcher who is
of the journey. Answer: 88.89 km 30. Allan gives Brando a head start of 5 seconds.
ahead by 72 of his own leaps. The snatcher
/ 15. Two trains started at the same time from cities Ans: 175 sec of Allan
takes 6 leaps while the cop takes 5 leaps, but 4
A and B, respectively, the first going from A to 31. Allan and Brando start at the same time.
leaps of the snatcher are as long as 3 leaps of the
Ans: 200 sec
Band the second from B to A. They traveled at cop. How many leaps will the cop make before
uniform but different rates. The first train he catches the snatcher? Police~n: 540 leaps
' .
M<1nila: https://www.facebook.corn/ReviewinnovationsOfficial Ceba FB: Excel-RI CE Review Specialist Inc. Davao: littps:I/www..facebook.com/reviewinnovations.davaobranrh
 Civil Engineering May 2019 ~ 1 l \ t>A"('L [~lffllliV INNOYITION! Algebra 1
SIGNIFICANT DIGITS: . BINOMIAL THEOREM: Motion in water current or air current
To ,t;nd the number of significant digits: If x = velocity of (boat/ airplane:) in 'itiJ!
(x + y)" = x" + nxn-1y1 + n(n-1) xn-2y2
Counting from left to right, start with the first non- 2! (water/ air) ~
zero digit and continue counting until the last digit; n(n - l)(n - 2) _ y = velocity of the (water/air), then
be it zero or not. + ----'-'---'-X 11 3 y3 + ... + nx1l-1+ l
. 3!
x + y = velocity when going (downstream/w ith the
EXPONENTS: wind)
Note: x - y = velocity when going (upstream/ against the
l. (a,,,) 11 = a"m
1. It starts with x 11 and ends with y11 • . wind)
2. Q,n X Q 11 = am-n 2. The power of x decreases by 1 while the power
a"' m-n of y increases by 1. Motion in a circle or any closed circuit
3. -=a 3. The sum of the powers of x & y in any term is Starting from the same point and the same time
. a"
always n. 1. Going in the same the direction:
4. al / n =¼ 4. There will be 11 + 1 terms in the expansion. d r.ster - d,1o wer = 1 circuit
- II 1 5. If the coefficient of a term is multiplied by the 2. Going in opposite directions:
5. a =-
a" power of x in that term and then the product d fa,ter + d, 1ower· =1 circuit
6. (axb)"' =a"'xb"' divided by the power of y increased by 1, the
resulting number is the coefficient of the next Problems:
term. -"'1. How many significant digits are there in
QUADRATIC EQUATION:
0.001040050? Answer: 7
Ax2 +Bx+C =0 ,-th Tenn of Binomial Expansion
✓2. If 8x = y, then what is 2 5x- 3 equal to in terms
th
Quadratic Formula r term in (x + y)" = C(n, m)x"-mym of y? Answer: ysn / 8
, 3. If the product of the roots of the quadratic
n! equation x2 + 2a:.x +a= 0 is equal to 3a + 6, find
X where m = r - 1 and C(rz, m)
(n-m) 1 m ! the sum of its roots. Answer: -18
/ 4, What is the value of k in'the equationh2 + 9x +
8 = 0 if the equation is to have only one root?
Roots of Quadratic Equation \
Answer: 81/ 32
-B+ ✓B 2 -4AC AGE-RELATED PROBLEMS
/ 5. Find the quadratic equation whose roots are the
2A
If x = -present age of a person reciprocals of the roots of the equation Ax2 + Bx
x - 3 = age of the person 3 years a~
+ C = 0. Answer: exi + Bx + A = O
x + 5 = age of the person 5 years hence
/ 6. Find the 6th term in the expansion of (2x3 + 9y) 11.
Note: The age-difference of t~vo persons is Answer: l,745,960,832Y18y5
Properties of Roots constant at any time. / 7. Find the constant term in the expansion of (x +
B x-3/2) 15. Answer: 5,005
Sum of the Roots: x1 + x 2 = - -
A / s . Find the sum of the coefficients of the ·terms in
C MOTION-RELATED PROBLEMS the expans_ion of (4.x - 7y) 4. Answer: 81
Product of the Roots: x 1 x 2 =-
A distance= velocity x time / 9, Four years ago, the sum of the ages of A and B
was 45. Six years from now, twice B's age will

Manila: htrps:/lwww.fa, ebook.com/ Reviewlnnovotion,O(ficinl Cebu FB: Ex<el-Rl CE Review Specinlist.f::'· ·oaYao: https:l/www.fa,ebook .com_lreviewinnovations.davaobranrh
' ~\J\cW : !\¼t6t\\ 1
.......__
fl.to,~ ; q i b

' (j) ~ ~i 'o

' @ : ab

'
'
' ll~ ~ ' tGx
"--t '0X-\ 1' -DJ

' - =- y~l?J ~ &1\\ ~ Or (cl'/1-t C\y')'

1

' 8 (atPJfl ; ~emo."4"\ 'oln .,f<\=r--\

'' rm "o ~c?-t itx t q
(ii, nc$; l~)( '1
\\-<o+\
("~1
(p-1

s
::; 4u~ o Cu~ xi~ • fllf C!;'ltOl\'\~
" \,~,'llJO,~?,· . ,_,~
' ~ CY.. + x:ofa_)\:!;

'I ~~ ~ a;;;-3
eGI • X.
• b::. '1--.Jti • ,~mt,
•1\~ •f(\::: 1

tx' =-- ~ CJln l 'f-'t'-t(\ ( £JfJ)"'-

' -1 :c@l ·l :, X~-wt ( ~--3taJ.
, . \B ~.,_+q'I- H "'O \
. :_
0 ::, \1--'ro- i
3M

\3 'l - Al\G .=:6 ~, vn ;; ~ ➔ '((\::: " ) r::: -=t

¥.=\&;GCo ; ~

'I '12 ___,,_. ' :::-0

~ s~ cf CQ-i"ff\U~i
\ • .S: G = ~I -+ ~1.Jn

I -
= f,\
.. (\<,tA +k2 b'{'
1

I U<O
u;;()
Q '7 0
~s~
l f\)>.~
~ UN~t\'L
 -~ ~ ~ ; V\ : ~ ~ s
X ' \JetbCtt'j CSf \? lQ\h\<.

- ~~")+(<3-4') =~ _, ~ -~?J -t\

(f\~)+l"o~ 1t0t<.i) _.
n- ~ '$ ~c~1,)
- t\ - ~ ~

-\-\i ::~
X(la/l)

- f\;,- '?J4 ~ \t)lp - <9-i -\'\'L

x;, 'b11 l";: e~
~

-
,~' ( ~~1~9-)
_.:::,__i,_.:.;..J_...:~~~ \~ +t~·ij)l'l-t~ i:::Vi- ~)i
3~;. Bi\
\11 ~ ::---\.1£ -\' '\\j
~
- ~,
e;. \~-;:~.

~~

-
C,~
M-\- f :: J( l CJ t(,~t_~) ')
~_j_--~----7
c\ \~,\-'\:~ ~ 1~
(M-~') --1(f-~I :: A( ~c-.s N; Ot-t~1 ·
"t t ~ ~ ~ ;a@s 14~\
\,io\
'•
:l'\

L-" -t ]
f-= o?t
f -\\J ~~cc-~)~ Jr:, -\o ~"'c -4\)N -0
c -tµ;;¼ ➔
-
~-: \I
~
"I \_,-V
Q.<tV
\!.ti (J.,-"l)/J_
-
....
\t\t---- = t o.<t\J

1
-

- P-t 30 :;, Jt-t?JD-::(1 \~~ -(;) 1 '\hr .

- ---
L~ ~-+1.Q.:!!
~L
\~r Q,<1.\J V c>;c,
'
\~( .,,
:2C., - ~"' +\O -=O ..
=.-'J- C>-CoL ::
-
.

1
__,;;_~+--d,__ - lc - ~ tao ~0)1. d' "~
v
1 - -\1.-S>
"IA\I

" () ,~\[
\C~~=O
t
'

---
'. \I~ · ((t,<,L.-'1~

• ~ l "~g\_

•I
I \.Co
'f{l.. Cf '6\~ ~ a_qy. ~---0)
iR 6f ~ ·. lcw. ~
~~ ;;~OX
I
i ~ lrt,\l(JU\'\\\ _,, (lqO\) -~11-C\/
I 20
<ft.l)f @ ~~ ,~ ~ ~ : \
"30 o.4L -0.4\J -~ ~o.s
so w. ~ l°i~ ~=~1@ ~T o(O}.}
OAL- 0.1(0.~\.) - o.~ .CQXc.~ .. ~
l@lC\O\) : 44 t-~ _@_ ;tee.ti~~
Q.B~~ --i
-~ ffi

-
-
-
-
' El -"iX- \'; :;C)\
'I
j

~ (4i-~J 8
•Q::: 4 f\i= ~

I ~ ➔ e ~ ?r\·4.-1 .,
,b::: -3 m=°i-\

, ~ =: ~c.m a
n..(\-\o \ t-\
b
1\-X X.
.
~➔~: ~ =1\~ ~nc ')t.l ka} l~1
'-~
?.,-t;],~~~~
~,<()

I 1"""\; ~o I t'
!

I ~
I

~1 !. t : 110 "X i '

-\ "-

I ~+ ~-r\3~
01) ~

~--x -= -\'3
I (Qt)

- ~::~
(90
I ~>!\
I .8 SY\M~ ~ c\ ,- 41 = 1Clfl.CU.l'\"
Of fc£\"re ~ d t f (\ 'l, :: \ ClU\.ltf
~It '9,.}'1 :, ~ -' \JI -\\f i c 30
I J.S\J I .. J9J ~~ \,t\) - \/1 - \J J. ,: (p

I ~ . ;r: 3C,
\\JI ~ \8) ~: \il
,~ ~ i v))( Un) ,.,. uu011n'i _,,,
n

I '<.-I t) • ?l ~

( X, -1{)(\ ~ ) " (oCJC;l"I - ' )( - I.\. "' 4DO

- --- ~ \X'''-2>x-a/t r-" [Q -t- bf
ll 'J_'J-. -;: -=r,&
•• \x ,; ?~.s\
• Q:: X
I/IJ..

• b :, _Jx-.$('1.
0 f\::: I'L

r ;:. W\ t t
•"'\ -: :-:

~
o

'tc).-"l -o/~rri
~ ki' .. \;l c.m()(v~ (-"11-- '
I \l - ~ - ~
0 -- -;r J J,
::. V\-
I ,, e=tCo\11
('J, W11.')(,\l\-Vi)
m= ~
--.,'-If
\<.•l ~ \1C0 l-9\
~

I ·~w,, ::: \4V ,1. -vtY-11. -<i)

\\l; ~~,
~ ('1?t;Jq')n ~ (0-VO/
/

I -
4 =
0
\J,-\Ji
Ir"'
'(\CJ/n.(l) ( i)J>t)
"'

-I
~1+~1 ,i l'l
('(\\ .. ~ ;- \ :: C'I. y ,
~\J , _:- t\'J i::: o\J 1 ·f3 V1
\J,,:,:; ~2.-©
·- 1. ' '1
~~
Git~1- ::: Co~ (Q\I ,z, - l ~ 1. ,~ ~ ~~-,r~:; ➔ n~vi.
-# Co
I ~,c ~ Ji8V/ \~"'" ~ ... ~-,,:-'If~ ~
f"-, :i 1M 'f

,\J~-;: \~\\i 1 c=~~<¼1\oi1" =t~,,o{pl

I @ ~
1trm\., ~ i\i\\\:f i -t 1:l ~(\/I -rJ 'L) := &JO 4 \J d \f d-"" \lfU
I
p

£..::, f :::~ \lQ( V, - Vs.") ::: 5DC) ~ V\ -\I ol ~~

-f\ ---eo <o
~, ~ \~
I R ~\° : 1· f t %)
, ;-~l
I -43
I ~
::::

-; . ,e,
--ST
(p

-t- , ~q(p
§ P1 ;:'9.m1\\.,
A 'Y -t;;u- \J
·\ ,~~ (9r~-\I /0"~\J 1
t= ~48
I \" ,,~ '16/ ~f\o]
\J \J O<p.., J

I
I
~ ; ~ ~
v1 :: ~ 1'11i ·, ,,. ;, t ; ~ ~ v
~ G)

': ct V ~-v
~ \t\r ~~~)/o:~'I 1

'
V V C>,%'-J

,.' -t
"
-x)N
·v
x/o.~ 1
c.~
I

'
w
- - - :.\.~
().~
I \~ =<l.3\a~ ~ )t.i\C _.:f.. ~,
-40 (S1)
I \J ::~.~
--,f
~X+ ~ =:uM)

I ~~ \~ :: \1& \

I ~ -ofi&x+x -% ;JJ;
0.991
I
0.~ ::: (QO.~U)~
I \ y.., ol43.~43~i \

I
I
I